Question

Find the solution of $x$ and $y$ using cross multiplication method:

$3x-y=1$ and $x+2y=5$

• A. $x=1,y=-2$
• B. $x=-1,y=2$
• C. $x=-1,y=-2$
• D. $x=1,y=2$

Answer 1

Answer: (D)

$x=1,y=2$

$3x-y=1$---(1)
$x+2y=5$---(2)
Using formula for cross multiplication method:
$\frac{x}{(b_1{c}_2-b_2{c}_1)}=\frac{y}{(c_1{a}_2-a_1{c}_2)}=\frac{-1}{(a_1{b}_2-a_2{b}_1)}$
So, from equation (1) and (2) we can write the value of$a,b$ and $c$.
$\frac{x}{-1\times 5-2\times 1}=\frac{y}{1\times 1-3\times 5}=\frac{-1}{3\times 2-1\times (-1)}$
$\frac{x}{-5-2}=\frac{y}{1-15}=\frac{-1}{6+1}$
$\frac{x}{-7}=\frac{y}{-14}=\frac{-1}{7}$
$\frac{x}{-7}=\frac{-1}{7}$
$7x=7$
$x=1$
$\frac{y}{-14}=\frac{-1}{7}$
$7y=14$
$y=2$
Therefore, $x=1,y=2$